Nematic Liquid Crystal — Topological Defect Texture

Frank elastic energy: F = K/2 ∫[(∇·n̂)² + (n̂×∇×n̂)²]d²r. Nematic order parameter has π₁(RP²)=Z₂, allowing half-integer (±1/2) defects. Pairs annihilate: +1/2 and −1/2 attract and collide.

Frank K 0.50 Noise 0.05

Director field: color = orientation, rods = local alignment